A company selling vegetable seeds in packets of 20 estimates...

A company selling vegetable seeds in packets of 20 estimates that the mean number of seeds that will actually grow is $18,$ with a standard deviation of 1.2 seeds. You buy 5 different seed packets. a) How many good seeds do you expect to get? b) What's the standard deviation? c) What assumptions did you make about the seeds? Do you think that assumption is warranted? Explain.

A company selling vegetable seeds in packets of 20 estimates that the mean number of seeds that will actually grow is $18,$ with a standard deviation of 1.2 seeds. You buy 5 different seed packets.
a) How many good seeds do you expect to get?
b) What's the standard deviation?
c) What assumptions did you make about the seeds? Do you think that assumption is warranted? Explain.

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Key Concepts

Expected Value

This is a statistical measure representing the average outcome of a random process if it were repeated many times. In problems like this, the expected value from multiple independent events is the sum of the individual expected values, which gives a predicted total outcome.

Variance and Standard Deviation

Standard deviation quantifies the amount of spread in the outcomes around the mean, and variance is the square of the standard deviation. When dealing with independent random variables, the variance of their sum is the sum of their individual variances, and the standard deviation of the sum is the square root of this total variance.

Independence Assumption

This is the assumption that outcomes from different events or trials do not affect each other. In this context, it means assuming that the number of seed sprouts in each packet is independent of the others, which allows us to add the variances directly when calculating the standard deviation of the total outcome.

Identically Distributed Variables

This concept refers to all random variables having the same probability distribution, which, in this case, means that each seed packet is assumed to have the same mean and standard deviation for the number of seeds that grow. This assumption simplifies the analysis and aggregation of results across multiple packets.

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